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17:55
Last 2 Digits
Mockat Admin17:55
Module 6 of 8
4.2 Last two digits
Questions around last two digits are less common in entrance tests. However, the concept is quite simple and easy to learn. The cases below are for finding the last two digits of a number where and are integers.4.2.1 x is a multiple of
Where , last digit of is and tens digit of x is even, the last two digits of .Where , last digit of is and tens digit of x is odd,
1) the last two digits of , where is even; and
2) the last two digits of , where is odd.
4.2.2 x is a multiple of
Where and last digit of is , the last two digits of4.2.3 x is a multiple of but not
Where is an integer, last two digits of last two digits of .We, therefore, split the powers and then individually multiply, as shown in the example below:
Example 18
What are the last two digits of ?
∴
Answer:
Solution
is a multiple of but not .∴
Answer:
4.2.4 x is a multiple of
Where is an integer, last two digits of last two digits of .Example 19
What are the last two digits of ?
is a multiple of .
∴
After this, we normally multiply the numbers to find the last two digits.
Answer:
Solution
We need to find .is a multiple of .
∴
After this, we normally multiply the numbers to find the last two digits.
Answer:
4.2.5 x is an odd number other than
When the units digit of a number is , then there is a cyclicity in the tens digit. Using this pattern, where the last digit of is , , or ,) Raise to a power such that the units digit becomes .
) The units digit of the resulting number raised to any power will always be .
) The tens digit of this number is the product of the tens digit of the base and the units digit of the power.
From steps and , if
Units digit of Tens digit of
Last digits of
Example 20
What are the last two digits of ?.
Units digit of
Tens digit of
∴
Answer:
Solution
Units digit of
Tens digit of
∴
Answer: